Investigation of a Homogeneous Many-Particle System in the Vicinity of the Critical Point

A theory based on a separate account of short-range repulsion and long-range attraction between particles is applied to the description of the liquid-gas critical point in the classical fluid case. The collective variables method with a reference system (RS) is used. Detailed investigation of the properties of RS cumulants makes it possible to transform the grand partition function into a functional form defined on the effective block lattice. The functional corresponds to the partition function of the Ising model in an external field. Then the collective variables method is used to calculate the Ising-model partition function in the vicinity of the phase transition point, which was developed in our previous papers. As a result one can separate reference system and long-range subsystem variables, which makes possible the quantitative solution of the liquid-gas critical point problem. The equation for the parameters of the critical point is obtained, as are explicit expressions for the equation of state both above and belowT c ; the chemical potential of the system is investigated.